12,521 research outputs found
The full Schwinger-Dyson tower for random tensor models
We treat random rank- tensor models as -dimensional quantum field
theories---tensor field theories (TFT)---and review some of their
non-perturbative methods. We classify the correlation functions of complex
tensor field theories by boundary graphs, sketch the derivation of the
Ward-Takahashi identity and stress its relevance in the derivation of the tower
of exact, analytic Schwinger-Dyson equations for all the correlation functions
(with connected boundary) of TFTs with quartic pillow-like interactions.Comment: Proceedings: Corfu 2017 Training School "Quantum Spacetime and
Physics Models
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
We study mixed weighted weak-type inequalities for families of functions,
which can be applied to study classical operators in harmonic analysis. Our
main theorem extends the key result from D. Cruz-Uribe, J.M. Martell and C.
Perez, Weighted weak-type inequalities and a conjecture of Sawyer, Int. Math.
Res. Not., V. 30, 2005, 1849-1871.Comment: Colloquium Mathematicum, to appea
Cellular Automata as a Model of Physical Systems
Cellular Automata (CA), as they are presented in the literature, are abstract
mathematical models of computation. In this pa- per we present an alternate
approach: using the CA as a model or theory of physical systems and devices.
While this approach abstracts away all details of the underlying physical
system, it remains faithful to the fact that there is an underlying physical
reality which it describes. This imposes certain restrictions on the types of
computations a CA can physically carry out, and the resources it needs to do
so. In this paper we explore these and other consequences of our
reformalization.Comment: To appear in the Proceedings of AUTOMATA 200
What is a quantum computer, and how do we build one?
The DiVincenzo criteria for implementing a quantum computer have been seminal
in focussing both experimental and theoretical research in quantum information
processing. These criteria were formulated specifically for the circuit model
of quantum computing. However, several new models for quantum computing
(paradigms) have been proposed that do not seem to fit the criteria well. The
question is therefore what are the general criteria for implementing quantum
computers. To this end, a formal operational definition of a quantum computer
is introduced. It is then shown that according to this definition a device is a
quantum computer if it obeys the following four criteria: Any quantum computer
must (1) have a quantum memory; (2) facilitate a controlled quantum evolution
of the quantum memory; (3) include a method for cooling the quantum memory; and
(4) provide a readout mechanism for subsets of the quantum memory. The criteria
are met when the device is scalable and operates fault-tolerantly. We discuss
various existing quantum computing paradigms, and how they fit within this
framework. Finally, we lay out a roadmap for selecting an avenue towards
building a quantum computer. This is summarized in a decision tree intended to
help experimentalists determine the most natural paradigm given a particular
physical implementation
Tornadoes in a Microchannel
In non-dilute colloidal suspensions, gradients in particle volume fraction
result in gradients in electrical conductivity and permittivity. An externally
applied electric field couples with gradients in electrical conductivity and
permittivity and, under some conditions, can result in electric body forces
that drive the flow unstable forming vortices. The experiments are conducted in
square 200 micron PDMS microfluidic channels. Colloidal suspensions consisted
of 0.01 volume fraction of 2 or 3 micron diameter polystyrene particles in 0.1
mM Phosphate buffer and 409 mM sucrose to match particle-solution density. AC
electric fields at 20 Hz and strength of 430 to 600 V/cm were used. We present
a fluid dynamics video that shows the evolution of the particle aggregation and
formation of vortical flow. Upon application of the field particles aggregate
forming particle chains and three dimensional structures. These particles form
rotating bands where the axis of rotation varies with time and can collide with
other rotating bands forming increasingly larger bands. Some groups become
vortices with a stable axis of rotation. Other phenomena showed include counter
rotating vortices, colliding vortices, and non-rotating particle bands with
internal waves
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